Explicit Hodge-Type Decomposition on Projective Complete Intersections

Abstract

We construct an explicit homotopy formula for the \(\bar{\partial }\)-complex on a reduced complete intersection subvariety \(V\subset {\mathbb {C}}{\mathbb {P}}^n\). This formula can be interpreted as an explicit Hodge-type decomposition for residual currents on V. As a first application of this formula we obtained the explicit Hodge decomposition on arbitrary Riemann surfaces.